Properties

Base field 3.3.316.1
Label 3.3.316.1-19.1-a
Conductor 19.1
Rank \( 1 \)

Related objects

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Base field 3.3.316.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 2 \); class number \(1\).

Elliptic curves in class 19.1-a over 3.3.316.1

Isogeny class 19.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
19.1-a1 \( \bigl[a\) , \( -1\) , \( 1\) , \( -2 a + 1\) , \( -a^{2} + 2 a - 1\bigr] \)
19.1-a2 \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph